Quantitative Methods for Gourmet Delight Restaurant

This report discusses the quantitative methods used to analyze the service times, advertising expenditure, restaurant takings, and patronage patterns of Gourmet Delight restaurant. It includes a regression analysis of advertising expenditure and revenue, a trend analysis of restaurant takings, and a comparison of service times before and after training. The report also discusses the patronage patterns of the restaurant.

Running Head: QUANTITATIVE METHODS
Quantitative Methods
Name of the Student
Name of the University
Student ID

1QUANTITATIVE METHODS
Table of Contents
Introduction................................................................................................................................2
Service Times Before Training and After Training...................................................................2
Advertising Expenditure............................................................................................................5
Restaurant Takings and Patronage.............................................................................................6
Patronage Patterns..................................................................................................................6
Trend of Restaurant Takings..................................................................................................7

2QUANTITATIVE METHODS
Introduction
Gourmet Delight is a fictitious five-star restaurant, which is locate in the Central
Business District in Melbourne. There is a sitting capacity of around 100 people at a time in
the restaurant. The restaurant is open from 12 pm – 3 pm for lunch and from 6 pm to 11 pm
for dinner. For all the seven days in a week, that is from Monday to Sunday, the restaurant
remains open. The owner of the restaurant has experienced a problem with the clients. He has
noticed eventually that the number of clients in the restaurant has been decreasing gradually.
He came to know that the service times to the customers has been extremely high for his
restaurant. This has been the reason for losing clients gradually. The clients had to wait for a
very long time to get served by the restaurant staffs. Thus, in order to retain the clients, the
owner of Gourmet Delight decided to conduct a training program for the staffs, so that the
service times are reduced. A service time of 20 minutes can be considered as an efficient
service. More than that will result in losing clients. Moreover, it has been observed that after
6 months of the training program, the number of staffs has been reducing, as they have been
leaving Gourmet Delight. Thus, it has to be estimated whether this is a matter of concern to
the owner of Gourmet Delight.
Service Times Before Training and After Training
An analysis of the service times to the clients has been performed. It has been
observed from the analysis that initially the staffs used to take more than 40 minutes on an
average to serve the customers. It has also been observed from the analysis that 50 percent of
the people have been served with a waiting time of more than 39.5 minutes, which is quite
high. Most of the people have been observed to wait for around 35 minutes to get served.
Thus, the estimated proper waiting time as stated by the owner has been greatly violated.
Hence, the training program. As can be seen from the analysis, the training program has

3QUANTITATIVE METHODS
greatly reduced the service times. The average time has been reduced to 20 minutes which is
what the target of the owner of Gourmet Delight was. It has also been observed that 50
percent of the clients had a service time less than 19 minutes. Most of the clients had been
found waiting for around 18 minutes. This is well within the satisfactory limit and thus it can
be said that the training program was of great help to the clients.
Table 1: Summary of Service Times
Serving Times prior to training
(minutes)
Serving Times after Training
(minutes)
Mean 40.53 20
Standard Error 1.75 1.21
Median 39.5 19
Mode 35 18
Standard
Deviation 9.59 6.65
Sample
Variance 92.05 44.28
Kurtosis 0.53 -0.86
Skewness 0.70 0.25
Range 40 24
Minimum 25 10
Maximum 65 34
Sum 1216 600
Count 30 30
Serving Times prior to training (minutes) Serving Times after Training (minutes)
0
10
20
30
40
50
Comparison of Serving Times Using Box and Whisker Plot
Serving Times
Figure 1: Box and Whisker Plot Showing Comparison
With the help of histograms also, a comparison of the service times has been
presented. From the histograms, it can be seen very clearly that after the training program, no
client was to wait for more than 40 minutes to get served at the restaurant, whereas, before

4QUANTITATIVE METHODS
the training, there were considerable number of clients who has to wait more than an hour to
get served.
15 25 35 45 55 65
0
2
4
6
8
10
12
14
16
Histogram Showing Serving Time (Prior Training)
Mid Point of Serving Times
Frequency
Figure 2: Serving Time Prior Training
15 25 35 45 55 65
0
2
4
6
8
10
12
14
16
Histogram Showing Serving Time (After Training)
Mid Point of Serving Times
Frequency
Figure 3: Serving Time After Training
Again, it has been observed that after 6 months, there has been a decrease in the
number of staffs in the restaurant. Now, the owner of the restaurant is thoughtful whether this
is a matter of concern or not. Thus, it has to be checked whether the service time at the
restaurant has increased after 6 months of providing the training. From the analysis, it has

5QUANTITATIVE METHODS
been observed that the service times has increased after 6 months. The average service time
has increased to 22.5 minutes, whereas 50 percent of the clients had to wait for more than 23
minutes to get served. The service time on an average has again increased from the estimated
good service time as stated by the owner, which is 20 minutes. Thus, it can be said that this
leaving of staffs might be a matter of concern for the owner of Gourmet Delight.
Table 2: Summary of Serving Time (6 months Late)
Mean 22.5
Standard Error 1.18
Median 23
Mode 20
Standard Deviation 5.26
Sample Variance 27.63
Kurtosis -1.15
Skewness -0.10
Range 17
Minimum 14
Maximum 31
Sum 450
Count 20
Serving Times after Training (minutes) Serving Time (6 months Late)
0
5
10
15
20
25
30
Serving times After Training and 6 Months Late
Serving Times
Figure 4: Box and Whisker Plot Showing Comparison
Advertising Expenditure

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It is important to advertise in the local press so as to have an increased patronage
about the restaurant. Thus, advertisement to offers such as “Two for the price of One” were
posted. For the past 18 months, all the advertisement expenditures for the company has been
obtained from the owner of the restaurant. The owner wanted to know whether the
expenditures on advertisement are significant on the revenue of the restaurant. A regression
analysis has been performed to obtain this result and from the analysis, it has been seen that
the advertisement expenditure is significant for the revenue earned by the restaurant (P-Value
less than 0.05). Hence, it can be said that with $1 increase in the advertisement cost, the
revenue earned by the restaurant increases by $7.45. This can be said with an accuracy of 84
percent.
Table 3: Regression on Revenue and Advertising Expenditures
Regression Statistics
Multiple R 0.92
R Square 0.84
Adjusted R Square 0.83
Standard Error 916.47
Observations 18
ANOVA
df SS MS F Significance F
Regression 1 71361889 71361888.58 84.964 0.000
Residual 16 13438585 839911.5647
Total 17 84800474
Coefficie
nts
Standard
Error
t
Stat
P-
value
Lower
95%
Upper
95%
Intercept 717.75 405.94
1.76
8 0.096 -142.79 1578.29
Advertising
Expenditure($) 7.45 0.81
9.21
8 0.000 5.74 9.16
Restaurant Takings and Patronage

7QUANTITATIVE METHODS
Patronage Patterns
The patterns of daily patronage have been shown with the help of the following
figure. From the figure it can be seen that there is almost a cyclical trend in the pattern of the
patronage at Gourmet Delight. From the original series pattern, it can be seen clearly that the
highest sale of the restaurant is observed on Fridays and Saturdays, whereas, the lowest sale
has been observed on Mondays. Thus, it can be said that after a whole tiring week, people
prefer to visit the restaurant on the weekends. The Sundays are less demanding as the next
day is again an office day. The least number of customers are observed on Mondays as it is
the first day of the week and every client will be busy with their office and will not be able to
spare quality time for the restaurants. The smoothing of the curve has shown a decrease in the
deviations of the number of customers who visit the restaurant. The trend shown with the
help of the smoothed series is a stable trend than the original trend.
Tues
Wed
Thur
Fri
Sat
Sun
Mon
Tues
Wed
Thur
Fri
Sat
Sun
Mon
Tues
Wed
Thur
Fri
Sat
Sun
Mon
Tues
Wed
Thur
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Tues
Wed
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1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031
0
20
40
60
80
100
120
140
Daily Patronage at Gourmet Delight
Number of
people who
were served a
meal
Smoothed
Series
Date and Day
Number of People
Figure 5: Patronage Patterns (Original and Smoothed Series)
Trend of Restaurant Takings
A prediction of the restaurant takings has to be conducted with the help of trend
analysis for the next four quarters. The prediction model has to be developed on the basis of
the data available for the previous period. The quarterly data on the undertakings of the

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restaurant are available till 2017, and the quarterly figures for the year 2018 has to be
predicted. A regression analysis has been conducted with the help of the available data to
develop this prediction model. The predicted takings of the restaurant for the four quarters of
2018 are illustrated with the help of a line chart given in figure 6. As it can be seen from the
predicted trend in the figure, the restaurant takings is supposed to increase in the quarters of
2018.
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
2014 2015 2016 2017 2018
$-
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
Predicted Restaurant Takings
Restaurant
takings
($'000s)(yi)
Predicted
Trend
Quarter and Year
Restaurant Takings
Figure 6: Predicted Restaurant Takings
The results of the trend analysis obtained with the help if regression conducted is
provide in table 4. From the table, the estimated trend equation that has been used for the
prediction of the future restaurant takings can be given by:
Quarterly Restaurant Takings=31.59+1.33 ×Time
Thus, it can be said that when there is no change in time, the quarterly restaurant
undertakings will be $3,159,000. Further, it can be said from the estimated equation that with
one-unit increase in the time or quarters, the restaurant undertakings increase by $1.33 times.
From the model developed, it can be seen that the p-value obtained is less than 0.05, which is
the level of significance. Hence, the model so developed is a significant prediction model

9QUANTITATIVE METHODS
with an accuracy of 63 percent (R-Square Value). The predicted undertakings are given in the
following table 5.
Table 4: Trend Analysis of Restaurant Takings
Regression Statistics
Multiple R 0.79
R Square 0.63
Adjusted R Square 0.60
Standard Error 5.04
Observations 16
ANOVA
df SS MS F Significance F
Regression 1 597.191 597.191 23.483 0.000
Residual 14 356.027 25.430
Total 15 953.217
Coefficient
s
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Intercept 31.59 2.64 11.946 0.000 25.92 37.26
Time 1.33 0.27 4.846 0.000 0.74 1.91
Year Quarter Restaurant Takings ($’000)
2018 1 $54.12
2 $55.45
3 $56.77
4 $58.10